Question

What is the remainder when 444^444^444 is divided by 7
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Answer 1

Answer:

1

Step-by-step explanation:

0

step 1 : Try to bring big no's into a form so that we get remainder of −1 or 1 , so that it will be easy for us to simplify

444=4∗111

as 1117 gives a remainder of −1 . So our goal of converting a bigger number to number which gives remainder 1 or −1 is attained and as

−1even=1

so

444x/7=(4x∗111x)/7=4x/7

(111x divided by 7   gives remainder of −1x which is equal to 1 as x is even )

Where

x=444444(even)

So

4x=4444444=2888444

step 2 : Observe the pattern of the remainders

20mod7=1

21mod7=2

22mod7=4

23mod7=1

24mod7=2

25mod7=4

so here, for a period of 3 remainder 1 repeats

here 888 is a multiple of 3 , so

2888 mod 7= 1

1444 mod 7= 1

Hence Answer is 1